Analytical modeling of part distortion in metal additive manufacturing

This work presents an analytical modeling methodology for the prediction of part distortion in powder bed metal additive manufacturing (PBMAM). The presented model consists of analytical thermal modeling, thermal stress modeling, residual stress modeling, and distortion modeling. It has promising short computational efficiency without resorting to finite element analysis or any iteration-based simulations. The temperature profile is calculated using a moving point heat source solution and heat sink solution with consideration of heat input from a moving laser and heat loss from boundary heat transfer. The thermal stress is calculated from the temperature calculation using a thermal stress model considering thermal load, surface tension, and hydrostatic pressure. The residual stress is calculated from the thermal stress calculation using an elastoplastic relaxation procedure. The residual stress–induced part distortion is finally calculated from the calculated residual stress and residual strain using a surface displacement model. The calculated part distortion was validated to experimental measurement on a twin-cantilever part produced by PBMAM of Ti6Al4V. Close agreements were observed. The computational time was recorded less than 10 s. The high predictive accuracy and high computational efficiency allow the process parameter planning for distortion control and elimination through inverse analysis.